DECOMPOSITION FOR GEOMETRICAL PRODUCTS

The work forming the basis of this application was undertaken over the past two decades. A publication list of authored and co-authored books, papers and special research documents has been compiled to represent the candidates’ work.

The main research work concerns decomposition for geometrical products. Decomposition here means expressing an entity as a combination of simpler components according to a predefined scale. This forms the basis of analysing that entity in order to interpret or explain. A geometrical product is any ‘manufactured’ product whose nature by definition contains, wholly or partially, a geometric description.

The main research consists of fundamental mathematics and philosophy for advanced metrology; geometrical computation; geometrical data analytics, and smart semantic systems. The main research on the foundations of decomposition is a major result and can be utilised for decomposition of geometrical products. Further Prof. Scott established the mathematics for stable segmentation, taking surface texture in a new and novel direction: Paul also recognised that category theory would be an ideal mathematical foundation for the semantic structure of knowledge. Overall the research is of practical utility through the generation of stable and robust solutions for industrial metrology.

Decomposition with subsequent analytics and semantic labelling represents the basis of a new paradigm shift in the metrology of geometrical products. This together with decomposition for smart semantic systems, for future use in manufacturing in readiness for smart autonomous factories (Industrie 4.0), is a vision of one possible future pathway for the specification, manufacture, and verification of geometrical products.